On the New Branch of Mathematical Science-Part 2

Abstract

The fifth Euclidean postulate problem in geometry is 2300 years old. This postulate is also known as Euclid’s parallel postulate. The great mathematicians tried their best to deduce the fifth postulate from the other four postulates. But unfortunately nobody could succeed in this geometrical battle. The studies devoted to this problem led to the origin of two non-Euclidean geometries. The authors resurveyed and established and gave a proof for this problem

Application of Sivasubramanian Kalimuthu Hypothesis to Triangles

“…Since we have derived (14) without assuming the fifth Euclidean postulate, Eq. 14 proves the parallel postulate [1][2][3] . But the mere existence of consistent models of Non-Euclidean geometries demonstrate the Euclid v cannot be deduced from Euclid I-Euclid IV.…”